The Φ-Martingale
(2015) , 31 pages
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- Abstract
- In this paper we focus on continuous martingales evolving in the unit interval [0,1]. We first review some results about the martingale property of solution to one-dimensional driftless stochastic differential equations. We then provide a simple way to construct and handle such processes. One of these martingales proves to be analytically tractable, and received the specific name of Φ- martingale. It is shown that up to shifting and rescaling constants, it is the only martingale (with the trivial constant, Brownian motion and Geometric Brownian motion) having a separable coefficient σ(t, x) = g(t)h(x) that can be obtained via a time-homogeneous mapping of Gaussian processes. The approach is applied to the modeling of stochastic survival probabilities.
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Citations
Vrins, F., & Jeanblanc, M. (2015). The Φ-Martingale (CORE Discussion Paper 2015/22). https://hdl.handle.net/2078.5/191348